Finite Group Databasebeta

← #25005993

Subgroups — #25005993

Order 11008.

490 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582764C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132538C214yesmaximal, complemented
4C43×#1463C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic
6C22×C4×Dic43C411yescharacteristic
7#14582863—21no—
8#14582764—21no—
9#14582764—21no—
10#14582764C412yes—
11#14582764C2212yes—
12C2×C43⋊#95—21no—
13C2×C43⋊#95—21no—
14#14582625—21no—
15#14582625C2212yes—
16C22×C4⋊C4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C2×#10621877—41no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43—41no—
26C2×C4⋊Dic43C2×C412yes—
27C2×C4×Dic43—21no—
28C2×C4×Dic43—24no—
29C2×C4×Dic43C2×C412yes—
30C22⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—41no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C2×M16×C43—41no—
40C2×C4⋊C4×C43—41no—
41C2×C4⋊C4×C43—41no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43D411yescharacteristic
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C4⋊C4×C43C2311yescharacteristic
46C22⋊C8×C43—22no—
47C22⋊C8×C43—41no—
48C24×C43C22⋊C411yescharacteristic
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—24no—
66C22×Dic43—22no—
67C22×Dic43—22no—
68C22×Dic43—42no—
69C22×Dic43—42no—
70C22×Dic43—44no—
71C22×Dic43—41no—
72C22×Dic43—41no—
73M16×C43—82no—
74C2×C8×C43—42no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊Dic43—42no—
80C4⋊Dic43—42no—
81C4×Dic43—24no—
82C4×Dic43—22no—
83C4×Dic43M1614yescomplemented
84#10621877—82no—
85C2×C43⋊C8—42no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43#9911yescharacteristic
91C23×C43#9911yescharacteristic
92C23×C43C2×C22⋊C411yescharacteristic
93C2×C4×C43—24no—
94C2×C4×C43—24no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—81no—
110C2×C4×C43—81no—
111C2×C4×C43#10112yes—
112C2×C4×C43C2×M1612yes—
113C2×Dic43—24no—
114C2×Dic43—48no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—44no—
118C2×Dic43—42no—
119C2×Dic43—82no—
120C2×Dic43—82no—
121C8×C43—82no—
122C43⋊C8—82no—
123#11511—431nomaximal, Sylow
124C22×C43—24no—
125C22×C43—24no—
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43#35412yes—
133C22×C43#35512yes—
134C22×C43#40711yescharacteristic
135C22×C43C2×#9911yescharacteristic
136C22×C43C2×#10111yescharacteristic
137C4×C43—22no—
138C4×C43—22no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43—41no—
143Dic43—44no—
144Dic43—82no—
145C2×#382—431no—
146#1463—431no—
147#1463D4311yescharacteristic
148#1324—434no—
149C2×C43—21no—
150C2×C43—22no—
151C2×C43—22no—
152C2×C43—21no—
153C2×C43#146311yescharacteristic
154C2×C43C2×#35411yescharacteristic
155C2×C43C2×#35511yescharacteristic
156C22×C4⋊C4—431no—
157C22×C4⋊C4C2×D4311yescharacteristic
158C22×C42—431no—
159#407—21no—
160#407—861no—
161#382—432no—
162#382—432no—
163#382—861no—
164#382—861no—
165C2×#95—861no—
166C2×#95—861no—
167#324—21no—
168#324—432no—
169#324—861no—
170#324C2×D4312yes—
171C43#1151111yescharacteristic, complemented, Sylow
172C23×C4—861no—
173C23×C4—861no—
174C23×C4C4×D4311yescharacteristic
175C23×C4D17211yescharacteristic
176C23×C4C22⋊D4311yescharacteristic
177C2×M16—41no—
178C2×M16—1721no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4—1721no—
184C2×C4⋊C4—1721no—
185C2×C4⋊C4C4×D4311yescharacteristic
186C2×C4⋊C4D17211yescharacteristic
187C2×C4⋊C4C22⋊D4311yescharacteristic
188C2×C4⋊C4C22×D4311yescharacteristic
189C2×C42—432no—
190C2×C42—864no—
191C2×C42—861no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—862no—
195C22⋊C8—1721no—
196#95—862no—
197#95—862no—
198#95—862no—
199#95—862no—
200C24(C2×D43)⋊C411yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—864no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4—1724no—
215C22×C4—1721no—
216C22×C4—1721no—
217C22×C4—1722no—
218C22×C4—1722no—
219C22×C4(C2×D43)⋊C411yescharacteristic
220C22×C4(C2×D43)⋊C411yescharacteristic
221C22×C4(C2×D43)⋊C411yescharacteristic
222C22×C4C2×C4×D4311yescharacteristic
223C22×C4C2×D17211yescharacteristic
224C22×C4C2×C22⋊D4311yescharacteristic
225M16—82no—
226M16—3442no—
227C2×C8—42no—
228C2×C8—1722no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—1722no—
234C4⋊C4—1722no—
235C42—434no—
236C42—864no—
237C42—862no—
238C23—21no—
239C23—21no—
240C23—22no—
241C23—22no—
242C23#1306323911yescharacteristic
243C23#1306323911yescharacteristic
244C23C2×(C2×D43)⋊C411yescharacteristic
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—864no—
264C2×C4—3442no—
265C2×C4—3442no—
266C2×C4—1724no—
267C2×C4—1722no—
268C2×C4—1728no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4#1306324312yes—
272C2×C4M16×D4312yes—
273C8—82no—
274C8—3442no—
275C22—24no—
276C22—24no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#1458269312yes—
284C22#1458269512yes—
285C22#1458286211yescharacteristic
286C22C2×#1306323911yescharacteristic
287C22C2×#1306324311yescharacteristic
288C4—22no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—3442no—
295C4—1724no—
296C2—21no—
297C2—21no—
298C2—22no—
299C2—22no—
300C2#1913292411yescharacteristic
301C2C2×#1458269311yescharacteristic
302C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1463C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1463D43
hypocenterC43#11511
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #19132538C2semidirect
83. C4×Dic43M16semidirect
171. C43#11511semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145827642
#191329252
#191325382
C43×#14632
#1151143